Abstract

We study multiple steady states in distillation. We first analyze the simplest case of ternary homogeneous azeotropic mixtures. We show that in the case of infinite reflux and an infinite number of trays (∞/∞ case) one can construct bifurcation diagrams on physical grounds with the distillate flow as the bifurcation parameter. Multiple steady states exist when the distillate flow varies non-monotonically along the continuation path of the bifurcation diagram. We derive a necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the distillation region boundaries. We also locate in the composition triangle the feed compositions that lead to these multiple steady states.
We further note that most of these results are independent of the thermodynamic model used. We show that the prediction of the existence of multiple steady states in the ∞/∞ case has relevant implications for columns operating at finite reflux and with a finite number of trays. Using numerically constructed bifurcation diagrams for specific examples, we show that these multiplicities tend to vanish for small columns and/or for low reflux flows. Nevertheless, the ∞/∞ multiplicities do exist for columns at realistic operating conditions. We comment on the effect of multiplicities on column design and operation for some specific examples.
We then extend the homogeneous mixture results to ternary heterogeneous mixtures. We study the ∞/∞ case in much more depth and detail by demonstrating how the ∞/∞ analysis can be applied to different column designs. More specifically, we show how the feasible distillate and bottom product paths can be located for tray or packed columns, with or without decanter and with different types of condenser and reboiler. We derive the fully detailed, necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the product paths. Simulation results for finite columns show that the predictions carry over to the finite case.
The complete list of the ∞/∞ case predictions is presented. The implications of these multiplicities for column design, synthesis and simulation are demonstrated. More specifically, we show how the ∞/∞ predictions can be useful for the selection of the entrainer, the equipment and the separation scheme. We show that, in some cases, the column operation at an unstable steady state may have some advantages. The important issue of the effect of the thermodynamic phase equilibrium on the existence of multiplicities is discussed. Using the ∞/∞ analysis, we identify entire mixture classes for which multiplicities are inherent and robust. Mixtures with ambiguous VLE data are studied; we show that in some cases a slight VLE difference between models and/or experimental data may affect the existence of multiplicities while other, major VLE discrepancies do not. Finally, we identify the key issues and the pitfalls one should be cautious about when designing or computing the composition profile of an azeotropic distillation column with a commercial simulator.

Item Type:

Report or Paper (Technical Report)

Additional Information:

Foremost, I wish to thank my advisor, Manfred Morari, for his continuous support, encouragement and guidance during my graduate studies, for his trust in my judgement and for allowing me ample freedom in conducting this work. His insightful comments, suggestions and criticism are greatly appreciated in and out of the professional sphere.
I wish to thank all my teachers at Caltech and especially Prof. Wiggins for his teaching of nonlinear dynamical systems and bifurcations; these courses inspired me to work on the subject that is now the title of my thesis. I would like to thank Prof. Gavalas and Prof. Brady for their interest in my work and future plans. I thank all three professors for their roles in my thesis committee.
During these six years at Caltech, many people have helped me directly through discussion and criticism of my work and indirectly through companionship and friendship.
I wish to thank all the members of the Morari group for their help and company along this "road" towards the completion of my Ph.D. Special thanks to my coworkers: Lionel Laroche, for his precious help and support at the early stages of my work at Caltech. Lionel was the perfect "senior group member;" without him, my "baptism of fire" into the world of graduate school research would not be so smooth and quick. George Meski, for his invaluable help with this project and the friendship, support and advice during the frustrating times of "job hunting." Cris Radu, for his assistance with AUTO. Thomas Güttinger (ETH, Zurich), whose three-week intense-training visit revitalized me for my final "sprint." Myung Wan Han, with whom, during the last months, I entered the realms of batch distillation. Working with all of you has been a true pleasure and a valuable experience.
I also want to thank the people (professors, staff and students) in the Chemical Engineering department at Caltech. Special thanks to Suresh Guptha for his immediate response to any computer-related problem and for his patience and help with all my questions and requests. I also thank Kathy Lewis and Adria McMillan for their help on various administrative matters.
I thank Prof. Gani (Danish Technical University, Lyngby) and Prof. Skogestad (Norwegian Technical University, Trondheim) for several enlightened discussions. I also thank Prof. Doherty and Jeffrey Knapp (University of Massachusetts, Amherst), Prof. Seider (University of Pennsylvania, Philadelphia) and Prof. Michelsen (Danish Technical University, Lyngby) for providing us thermodynamic data and subroutines.
I gratefully acknowledge the financial support of the I. S. Latsis Foundation which, for ten years now (since my first days at the National Technical University of Athens), has continuously supported me during my undergraduate and graduate studies. The financial support of the Donors of the Petroleum Research Fund administered by the American Chemical Society is greatly appreciated.
I wish to thank Mike Linden-Martin for the excellent "English in everyday life" courses (the only literally fun Caltech courses); my english would be much worse without the in depth, frame by frame, analysis of episodes of "Married with children". I also thank the people at the International Student Programs for their help with all the INS and IRS related issues.
Turning to the indirect, non-academic but equally important contributions, I want to thank my family - grandfather and grandmothers, aunts, uncles and cousins - and foremost my parents, Yanni and Maria, and my brothers, Apostoli and Vassili, for their love, care and continuous support and for everything they have done for me. I will never forget my parents' moral support during some difficult times at Caltech (in the very beginning and at the end), the 2 a.m. "talk" sessions with my brothers and their commitment to updating me about family news via electronic mail, my grandfather's calendars, Tzela's and Dimitris' letters and tapes, Froso's and Elpida's pine nuts ("I told you, I don't like them," ) ... It is because of you that I contributed (and I will continue to contribute) to the welfare of the long-distance telephone companies.
I want to thank my friends and classmates from "Polytechnio" (NTUA) and especially Costas Bokis, Kostas Konstantopoulos and Christos Dalianis who also came to the U.S. to pursue a higher level of education, for the numerous discussions about common concerns and problems. I want to thank the friends I left in Greece, and particularly Yannis Koutsikos whose friendship will always be there, although we have not seen each other for six years.
Finally, I want to thank all the new friends I made at Caltech and in Los Angeles for the great time we had together - from the early lunch-breaks at the Athenaeum to the Hellenic Association meetings and parties of the 1991-1993 era and from the "clubbings" at Kontrol Faktory and Sin-a-matic to the latest Red Door Cafk coffee breaks (John Yamasaki, you are here). Special thanks to Chrisa Economou, Vassilis Hatzimanikatis, Sophia Kyriazopoulou, Gautam Vasisht, Sarah Jones, Yorgos "Malik" Stylianos, Thanos Tsirukis, Vicky Papageorgaki, Polly Preventza, Dimitris Kallifatides, Panos Pantzicas, Petros Mouchtaris, Yannis and Erotokritos Katsavounides, Miltos Papalexandris, for contributing, one way or another, to my growth and my better understanding of what I want from life. Last but not least, I want to thank Andri Zapiti for her love and patience and for being a constant source of moral support during the last two years.